Solvability of Linear Electrical Networks

Abstract

The problem of the solvability of a linear active network is discussed on the basis of the two-graph method. It is shown that the topological condition for the solvability is the existence of a common tree of the voltage and current graphs derived from the network. Several conditions for the existence of a common tree are given as well as an algorithm to check whether a common tree exists or not. The algorithm also gives a common tree, if one exists. Then a structure of two-graphs is defined and algorithms to determine the structure are given. The uniqueness and the stability of the structure are discussed. A decomposition of the coefficient matrix of the network equations is derived from the structure. Finally, a classification of the network solvability is given.